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d
ap
p
licatio
n
s
,
s
o
it
r
eq
u
ir
es
v
ar
iab
le
v
o
lta
g
e
w
h
ic
h
ca
n
b
e
o
b
tain
ed
th
r
o
u
g
h
NP
C
i
n
v
er
ter
.
Fo
r
th
i
s
t
y
p
e
o
f
ap
p
licatio
n
s
,
in
v
er
ter
u
s
ed
w
it
h
s
y
m
m
e
tr
ic
v
o
ltag
e
m
a
g
n
i
tu
d
e
an
d
f
r
eq
u
e
n
c
y
a
n
d
n
ee
d
s
o
f
lar
g
e
d
c
lin
k
ca
p
ac
ito
r
s
an
d
r
ec
tif
ier
cir
cu
it
[
1
5
]
.
T
h
e
p
r
o
p
o
s
ed
s
y
s
te
m
ex
p
lai
n
s
th
e
SVP
W
M
f
o
r
3
-
p
h
ase
3
-
le
v
el
Ne
u
tr
al
P
o
in
t
C
la
m
p
ed
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er
ter
f
ed
in
d
u
ctio
n
m
o
to
r
co
n
tr
o
l,
w
h
ic
h
lead
s
to
m
in
i
m
is
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t
h
e
s
tato
r
cu
r
r
en
t
an
d
to
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ce
T
HD.
Mu
ltil
e
v
el
in
v
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ter
s
ar
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m
u
c
h
m
o
r
e
s
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itab
le
f
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ctio
n
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o
to
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tr
o
l,
w
h
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p
r
o
v
id
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ea
r
l
y
s
i
n
u
s
o
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u
tp
u
t
v
o
lta
g
e.
T
h
e
p
r
o
p
o
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ed
s
y
s
te
m
s
i
m
u
latio
n
ar
e
v
er
if
ied
u
s
i
n
g
m
atlab
s
i
m
u
li
n
k
.
2.
3
-
L
E
VE
L
N
E
UT
RAL P
O
I
N
T
CL
AM
P
E
D
(
NP
C)
I
NV
E
RT
E
R
NP
C
m
u
l
tilev
e
l
in
v
er
ter
s
s
y
n
t
h
esize
t
h
e
s
m
a
ll
s
tep
o
f
s
tair
c
ase
o
u
tp
u
t
v
o
lta
g
e
f
r
o
m
s
e
v
er
al
lev
els
o
f
DC
ca
p
ac
ito
r
v
o
ltag
es
[
1
6
]
.
A
k
-
le
v
el
NP
C
-
M
L
I
in
v
er
ter
co
n
s
i
s
ts
o
f
(
k
-
1
)
ca
p
ac
ito
r
s
o
n
th
e
DC
b
u
s
lin
k
,
2
(
k
-
1
)
p
o
w
er
s
w
itc
h
in
g
d
ev
ice
s
p
er
p
h
ase
an
d
2
(
k
-
2
)
cla
m
p
in
g
d
io
d
es
p
e
r
p
h
as
e.
I
n
[
1
7
]
th
e
DC
b
u
s
v
o
lta
g
e
is
s
p
lit
in
to
3
lev
els
b
y
u
s
in
g
2
DC
ca
p
ac
ito
r
s
,
C
1
an
d
C
2
.
E
ac
h
ca
p
ac
ito
r
d
iv
id
es
v
o
ltag
e
as
Vd
c/2
v
o
lts
an
d
v
o
ltag
e
s
tr
ess
w
i
ll
b
e
li
m
i
ted
to
o
n
e
ca
p
ac
ito
r
lev
el
th
r
o
u
g
h
cla
m
p
in
g
d
io
d
es
[
1
8
]
.
T
h
e
Fig
u
r
e
1
s
h
o
w
s
t
h
e
3
lev
el
3
p
h
ase
NP
C
-
i
n
v
er
ter
.
I
n
th
i
s
p
r
o
p
o
s
ed
s
y
s
te
m
,
w
h
i
ch
co
n
s
i
s
ts
o
f
3
p
h
ases
(
3
le
g
s
)
an
d
ea
c
h
p
h
ase
co
n
tain
s
4
s
w
itc
h
es.
Fro
m
t
h
e
Fig
u
r
e,
ea
ch
le
g
ca
n
b
e
o
p
er
ated
in
3
s
w
i
tch
i
n
g
s
tate
s
li
k
e
+V
d
c/2
,
0
,
-
Vd
c/2
.
Fi
g
u
r
e
1
.
C
ir
cu
it d
ia
g
r
a
m
o
f
3
-
le
v
el
NP
C
in
v
er
ter
(
a)
(
b
)
Fig
u
r
e
2
.
Mo
d
es o
f
o
p
er
atio
n
(
a)
-
1
-
1
1
(
b
)
1
-
10
T
h
e
m
o
d
es
o
f
o
p
er
atio
n
s
o
f
3
-
p
h
ase
3
-
le
v
el
n
e
u
tr
al
p
o
in
t
cla
m
p
ed
(
NP
C
)
in
v
er
ter
w
it
h
o
u
tp
u
t
v
o
ltag
e
le
v
el
s
ar
e
s
h
o
w
n
in
F
i
g
u
r
e
2.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4752
P
a
p
er S
V
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W
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r
3
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p
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s
e
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l P
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in
t Cl
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r
ter fed
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n
d
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ctio
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Mo
to
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R
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P
a
la
n
is
a
my
)
705
a)
T
h
e
Fig
u
r
e
2
a
(
-
1
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1
1
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s
h
o
w
s
th
e
s
w
i
tch
e
s
S
3
&
S
4
ar
e
ON
in
leg
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1
,
s
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th
e
o
u
tp
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t
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V
dc
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T
h
e
s
w
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s
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3
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4
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e
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o
th
e
o
u
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u
t
v
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l
tag
e
is
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V
dc
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V.
an
d
in
leg
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3
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e
s
w
itc
h
es
S
1
&
S
2
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e
ON,
w
h
ich
lead
s
to
+V
dc
/2
V.
b
)
Fig
u
r
e
2b
(1
-
1
0
)
s
h
o
w
s
th
e
s
w
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h
es
S
1
&
S
2
ar
e
ON
i
n
l
eg
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1
,
s
o
t
h
e
o
u
tp
u
t
v
o
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e
is
+V
dc
/2
V.
T
h
e
s
w
itch
e
s
S
3
an
d
S
4
ar
e
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N
in
leg
-
2
,
th
e
o
u
tp
u
t v
o
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g
e
is
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V
dc
/2
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d
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g
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3
t
h
e
s
w
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tc
h
es
S
2
&
S
3
ar
e
ON,
w
h
ic
h
lead
s
to
0
V.
3
.
SPAC
E
VE
CT
O
R
P
U
L
SE
W
I
DT
H
M
O
DUL
AT
I
O
N
(
SVPWM
)
SVP
W
M
is
a
co
n
tr
o
l
tech
n
iq
u
e
f
o
r
th
e
M
L
I
s
w
i
tch
e
s
w
h
i
ch
id
en
ti
f
ie
s
th
e
s
w
itc
h
i
n
g
s
e
q
u
en
ce
s
b
y
p
lace
m
en
t
o
f
a
s
w
itc
h
i
n
g
v
e
cto
r
in
d
-
q
s
p
ac
e.
I
t
is
b
etter
at
h
ar
m
o
n
ic
lev
el
r
ed
u
ctio
n
an
d
in
cr
ea
s
in
g
th
e
o
u
tp
u
t
v
o
lta
g
e
m
ag
n
it
u
d
e
as
c
o
m
p
ar
ed
to
SP
W
M
(
Sin
u
s
o
id
al
P
u
ls
e
W
id
th
Mo
d
u
latio
n
)
,
w
h
ic
h
is
co
m
m
o
n
l
y
u
s
ed
.
I
t
r
ed
u
ce
s
th
e
co
m
m
o
n
m
o
d
e
v
o
lta
g
e
w
h
ich
is
t
h
e
d
i
f
f
er
en
ce
b
et
w
ee
n
v
ec
to
r
s
u
m
o
f
th
e
p
o
ten
tial
a
t
in
v
er
ter
o
u
tp
u
t
an
d
g
r
o
u
n
d
.
R
ed
u
ci
n
g
it
i
m
p
r
o
v
es
in
v
er
te
r
ef
f
icie
n
c
y
.
T
h
e
v
o
ltag
e
s
ac
r
o
s
s
th
e
t
w
o
d
c
lin
k
ca
p
ac
ito
r
s
s
h
o
u
ld
id
ea
ll
y
b
e
eq
u
all
y
d
i
v
id
ed
,
b
u
t
d
u
e
to
ca
p
ac
ito
r
leak
ag
e
c
u
r
r
en
t
t
h
er
e
is
a
v
o
ltag
e
u
n
b
ala
n
ce
w
h
ic
h
p
r
o
d
u
ce
s
s
tr
ess
o
n
th
e
s
w
itc
h
e
s
.
Fo
r
d
eter
m
in
in
g
th
e
s
w
i
tch
i
n
g
s
tate,
t
h
e
s
p
ac
e
v
ec
to
r
d
iag
r
a
m
is
d
iv
id
ed
i
n
to
s
i
x
s
ec
to
r
s
,
e
ac
h
h
av
i
n
g
f
o
u
r
tr
ian
g
le
s
.
E
ac
h
j
u
n
ct
io
n
p
o
i
n
t
r
e
f
er
s
to
a
s
w
it
ch
in
g
s
tate.
Fo
r
an
n
le
v
el
in
v
er
ter
,
n
3
s
w
i
tch
in
g
s
tates a
r
e
p
o
s
s
ib
le.
T
w
e
n
t
y
s
e
v
en
s
w
itc
h
i
n
g
s
tates
f
o
r
a
th
r
ee
lev
el
in
v
er
ter
ar
e
s
h
o
w
n
in
F
ig
u
r
e
3.
Fig
u
r
e
3
.
S
w
i
tch
i
n
g
s
tate
s
&
v
ec
to
r
s
Sp
ac
e
v
ec
to
r
P
W
M
B
ased
o
n
th
e
r
ef
er
e
n
ce
v
o
lta
g
e
lev
e
l,
th
e
s
p
ac
e
v
ec
to
r
m
ag
n
i
tu
d
e
a
n
d
p
lace
m
en
t
in
o
n
e
o
f
t
h
e
tr
ian
g
les
o
f
o
n
e
o
f
th
e
s
i
x
s
ec
t
o
r
s
is
d
eter
m
in
ed
u
s
in
g
ab
c
-
d
q
co
n
v
er
s
io
n
.
T
h
e
s
w
i
tch
i
n
g
s
tate
d
ep
en
d
s
o
n
th
e
s
p
ac
e
v
ec
to
r
p
o
s
itio
n
o
b
tain
ed
.
A
f
ter
ca
lc
u
lat
io
n
o
f
t
h
e
s
m
a
l
l
tr
ian
g
le
w
e
n
ee
d
to
ca
lcu
late
its
s
w
itc
h
i
n
g
ti
m
e.
T
h
e
s
w
itch
in
g
t
i
m
e
w
o
u
ld
b
e
th
e
s
a
m
e
f
r
o
m
V
dx
,V
qx
r
e
f
er
en
ce
s
i
n
ce
t
h
e
v
ec
to
r
p
o
in
ti
n
g
at
V
d
,V
q
r
e
m
ai
n
s
t
h
e
s
a
m
e,
o
n
l
y
i
ts
a
x
is
is
s
h
i
f
ted
.
L
et
T
M1
,T
M3
,T
M4
b
e
th
e
s
w
i
tch
i
n
g
ti
m
e
s
f
o
r
th
e
t
h
r
ee
v
e
r
tices
o
f
t
h
e
s
m
al
l
tr
ian
g
le,
w
h
ic
h
is
s
h
o
w
n
in
Fi
g
u
r
e
4.
Fig
u
r
e
4
.
S
w
i
tch
i
n
g
ti
m
e
ca
lc
u
latio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4752
I
n
d
o
n
esia
n
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l
.
9
,
No
.
3
,
Ma
r
ch
2
0
1
8
:
7
0
3
–
7
1
0
706
T
=
T
M1
+T
M3
+T
M4
(
1
)
w
h
er
e
T
is
th
e
to
tal
s
w
itc
h
i
n
g
ti
m
e.
T
h
e
v
o
lt
-
ti
m
e
b
alan
ce
eq
u
a
tio
n
is
,
V‘
T
=V
M3
T
M3
+V
M4
T
M4
(
2
)
T
h
e
p
o
s
itio
n
o
f
M3
an
d
M4
w
.
r
.
t
M1
is
(
1
,
0
)
an
d
(
0
.
5
,
h
)
r
esp
ec
tiv
el
y
.
S
u
b
s
tit
u
ti
n
g
th
e
s
e
v
al
u
es
o
f
m
ag
n
it
u
d
e
in
t
h
e
ab
o
v
e
eq
u
ati
o
n
w
e
g
et
V
dx
T
=
T
M3
+0
.
5
T
M4
(
3
)
V
qx
T
=
T
M4
h
(
4
)
T
M4
= V
qx
T
/h
(
5
)
an
d
T
M3
=
T
(
V
dx
-
0
.
5
V
qx
/h
)
(
6
)
an
d
T
M1
=T
-
(T
M4
+
T
M3
)
(
7
)
T
h
e
s
w
itc
h
i
n
g
t
i
m
e
f
o
r
th
e
o
th
er
tr
ian
g
le
s
ca
n
b
e
ca
lcu
lated
u
s
i
n
g
th
e
s
a
m
e
ab
o
v
e
eq
u
at
io
n
s
.
4.
SI
M
UL
AT
I
O
N
R
E
SU
L
T
S
AND
DIS
C
USS
I
O
N
T
o
v
alid
ate
th
e
p
er
f
o
r
m
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[1
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R.
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u
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ta,
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o
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[2
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R.
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.
[3
]
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2
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[7
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R.
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a
lan
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y
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y
a
k
u
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m
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r,
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m
a
c
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e
c
ted
P
V
S
y
ste
m
‖
,
In
d
ia
n
J
o
u
r
n
a
l
o
f
S
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ien
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
2
0
1
6
No
v
,
9
(
4
2
)
.
[8
]
Y.
Ca
i,
C.
W
a
n
g
,
F
.
Zh
a
o
,
a
n
d
R
.
Do
n
g
,
“
De
sig
n
o
f
a
h
ig
h
-
fr
e
q
u
e
n
c
y
iso
la
ted
DTHB
c
L
L
C
b
id
ire
c
ti
o
n
a
l
re
so
n
a
n
t
DC
-
DC c
o
n
v
e
rte
r,”
in
P
r
o
c
.
IE
E
E
Co
n
f
.
T
ra
n
sp
.
El
e
c
tri
f
ica
ti
o
n
A
sia
-
P
a
c
.
,
2
0
1
4
,
p
p
.
1
–
6.
[9
]
D.
Y.
Kim
,
J.
K.
Ki
m
,
a
n
d
G
.
-
W
.
M
o
o
n
,
―
A
th
re
e
-
lev
e
l
c
o
n
v
e
rter
with
re
d
u
c
e
d
f
il
ter size
u
sin
g
tw
o
tr
a
n
sf
o
r
m
e
rs
a
n
d
f
l
y
in
g
c
a
p
a
c
it
o
rs,‖
IEE
E
T
r
a
n
s.
P
o
we
r E
lec
tro
n
.
,
v
o
l.
2
8
,
n
o
.
1
,
p
p
.
4
6
–
5
3
,
Ja
n
.
2
0
1
3
.
[1
0
]
R.
P
a
lan
isa
m
y
,
K.
V
ij
a
y
a
k
u
m
a
r
―
M
a
x
i
m
u
m
o
o
st
o
n
tro
l
f
o
r
7
-
lev
e
l
z
-
so
u
rc
e
c
a
sc
a
d
e
d
h
-
b
r
id
g
e
in
v
e
rter
‖
,
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
r E
lec
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
P
EDS
)
,
v
o
l
8
,
Iss
u
e
2
,
Ju
n
e
2
0
1
7
.
[1
1
]
P
o
h
Ch
ian
g
L
o
h
,
F
e
n
g
Ga
o
,
F
re
d
e
Blaa
b
jerg
,
a
n
d
S
o
k
we
il
i
m
.
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e
r
a
ti
o
n
a
l
A
n
a
l
y
sis
a
n
d
M
o
d
u
lati
o
n
Co
n
tr
o
l
o
f
T
h
re
e
L
e
v
e
l
Z
-
S
o
u
rc
e
In
v
e
rters
w
it
h
En
h
a
n
c
e
d
Ou
tp
u
t
W
a
v
e
f
o
r
m
Qu
a
li
ty
.
IEE
E
T
ra
n
sa
c
ti
o
n
o
n
Po
we
r
El
e
c
tro
n
ics
,
Ju
ly
2
0
1
0
.
Vo
l.
2
4
,
No
.
7
.
[1
2
]
R.
P
a
lan
isa
m
y
,
A
.
U
M
u
taw
a
k
k
il
,
K.
V
ij
a
y
a
k
u
m
a
r
―
H
y
ste
re
sis
S
V
M
f
o
r
c
o
u
p
led
i
n
d
u
c
to
r
z
so
u
rc
e
d
io
d
e
c
lam
p
e
d
3
-
lev
e
l
in
v
e
rter
b
a
se
d
g
rid
c
o
n
n
e
c
ted
P
V
sy
ste
m
‖
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
m
s
(
IJ
PE
DS
)
,
v
o
l
7
,
Is
s
u
e
4
,
De
c
2
0
1
6
.
[1
3
]
H.
S
h
in
o
h
a
ra
,
K.
Kim
o
to
,
T
.
Ita
m
i,
T
.
Am
b
o
u
,
C.
Ok
a
d
o
,
K.
Na
k
a
ji
m
a
,
S
.
Ho
jo
,
K.
O
w
a
d
a
,
M
.
Ku
n
iy
o
sh
i,
a
n
d
Y.
S
a
to
,
“
De
v
e
lo
p
me
n
t
o
f
a
re
sid
e
n
ti
a
l
u
se
,
u
ti
li
ty
in
ter
a
c
t
ive
PV
i
n
v
e
rte
r
wit
h
iso
l
a
ti
o
n
tra
n
sf
o
rm
e
r
-
les
s
c
irc
u
it
—
De
v
e
lo
p
me
n
t
a
sp
e
c
t
s,”
in
P
ro
c
.
I
EE
E
P
h
o
t
o
v
o
lt
.
S
p
e
c
.
C
o
n
f
.
,
2
0
0
9
,
p
p
.
1
2
1
6
–
1
2
1
8
.
[1
4
]
E.
G
u
b
ra
,
P
.
S
a
n
c
h
is,
A
.
Urs
u
a
,
J.
L
o
p
e
z
,
a
n
d
L
.
M
a
rr
o
y
o
,
―
G
ro
u
n
d
c
u
rre
n
ts
i
n
sin
g
le
-
p
h
a
se
tran
sf
o
rm
e
rles
s
p
h
o
to
v
o
lt
a
ic sy
ste
m
s,‖
P
ro
g
.
P
h
o
t
o
v
o
lt
.
:
Re
s.
A
p
p
l
.
,
p
p
.
6
2
9
–
6
5
0
,
M
a
y
2
0
0
9
.
[1
5
]
O.
L
o
p
e
z
,
R.
T
e
o
d
o
re
sc
u
,
F
.
F
r
e
ij
e
d
o
,
a
n
d
J.
D
o
v
a
l
-
G
a
n
d
o
y
,
“
El
imin
a
ti
n
g
g
r
o
u
n
d
c
u
rr
e
n
t
i
n
a
tra
n
sf
o
rm
e
rle
ss
p
h
o
to
v
o
lt
a
ic
a
p
p
li
c
a
t
io
n
,
”
in
P
ro
c
.
IEE
E
P
o
w
e
r
En
g
.
S
o
c
.
G
e
n
.
M
e
e
t.
,
p
p
.
1
–
5
,
Ju
n
.
2
0
0
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
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I
n
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9
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3
,
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r
ch
2
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:
7
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–
7
1
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710
[1
6
]
T
.
Ke
r
e
k
e
s,
R.
T
e
o
d
o
re
sc
u
,
a
n
d
M
.
L
ise
rre
,
―
E
v
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lu
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ti
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n
o
f
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re
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p
h
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se
tran
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o
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m
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s
p
h
o
t
o
v
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lt
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ic
in
v
e
rter
to
p
o
lo
g
ies
,
‖
IEE
E
T
ra
n
s.
P
o
we
r
El
e
c
tro
n
.
,
v
o
l.
2
4
,
n
o
.
9
,
p
p
.
2
2
0
2
–
2
2
1
1
,
S
e
p
.
2
0
1
2
.
[1
7
]
H.
F
.
X
iao
a
n
d
S
.
J.
X
ie,
―
L
e
a
k
a
g
e
c
u
rre
n
t
a
n
a
l
y
ti
c
a
l
m
o
d
e
l
a
n
d
a
p
p
l
ica
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o
n
i
n
sin
g
le
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p
h
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se
tran
sf
o
r
m
e
rles
s
p
h
o
to
v
o
lt
a
ic g
rid
-
c
o
n
n
e
c
ted
in
v
e
r
ter,‖
IEE
E
T
r
a
n
s.
El
e
c
tro
ma
g
n
.
C
o
mp
a
t
.
,
v
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l
.
5
2
,
n
o
.
4
,
p
p
.
9
0
2
–
9
1
3
,
No
v
.
2
0
1
0
.
[1
8
]
P
a
lan
isa
m
y
,
R.
,
V
i
jay
a
k
u
m
a
r,
K.
,
Ba
g
c
h
i,
A
.
,
G
u
p
ta,
V
.
,
S
i
n
h
a
,
S
.
"
I
m
p
le
m
e
n
tatio
n
o
f
c
o
u
p
led
in
d
u
c
to
r
b
a
se
d
7
-
lev
e
l
in
v
e
rter
w
it
h
re
d
u
c
e
d
s
w
it
c
h
e
s
‖,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Po
we
r
El
e
c
tro
n
ics
a
n
d
Dr
ive
S
y
ste
ms
(
IJ
PE
DS
)
,
8
(3
),
p
p
.
1
2
9
4
-
1
3
0
3
,
2
0
1
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.